Sparse SIR: Optimal rates and adaptive estimation
从决策理论角度研究稀疏切片逆回归的极小化最优收敛速率，提出计算可行且速率最优的自适应估计方法，对高维数据降维研究者和实践者有参考价值。
Sliced inverse regression (SIR) is an innovative and effective method for sufficient dimension reduction and data visualization. Recently, an impressive range of penalized SIR methods has been proposed to estimate the central subspace in a sparse fashion. Nonetheless, few of them considered the sparse sufficient dimension reduction from a decision-theoretic point of view. To address this issue, we in this paper establish the minimax rates of convergence for estimating the sparse SIR directions under various commonly used loss functions in the literature of sufficient dimension reduction. We also discover the possible trade-off between statistical guarantee and computational performance for sparse SIR. We finally propose an adaptive estimation scheme for sparse SIR which is computationally tractable and rate optimal. Numerical studies are carried out to confirm the theoretical properties of our proposed methods.